VDU_Physics_3_005

## Solved University-Physics Problems

Physics 3:  Introduction to Electricity & Magnetism

## <<<  Electric Field between parallel plates  >>>

Javier Montenegro Joo

## jmj@VirtualDynamics.Org

<<<  Electric Field between parallel plates   >>>

(1) Two rectangular plates of sides “a” and “b” are placed so that an upwards vertical electric field “Eo” is established between both. Calculate the electric charge in each plate.

Solution.-

In order to find the connection between the electric field Eo between the plates and the charge on a plate consider a Gaussian surface as it is shown in the sketch:

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(2) In the region between two parallel plates separated by a distance d and loaded with opposite electric charges, a horizontal and uniform electric field has been established.  A little ball of mass m and positive electric charge Qo,  is placed at rest at the positive plate.  Sometime t later the ball hits the negative plate. Ignoring the effects of the Gravity, determine (a) the magnitude of the electric field (b) the velocity of the little ball when it hits the negative plate. (c) The kinetic energy of the charged particle when arriving at the negative plate.

Solution

Once the positively charged ball is placed close to the positive plate the former is repelled by the repulsive electrical force of the latter, hence the ball acquires acceleration. According to Newton     F = ma    and  electric field is   E = F/Q   then:

(3) In a place where the acceleration of the gravity is    12 m/s2  , an object having an electric charge of   0.000033 C    is placed between two parallel slabs with opposite charges, which setup a uniform vertical electric field of  750 N/C. Determine: (a) The mass of the object if this floats motionless in the field  (b) The magnitude that the electric field should have so that the object acquires an acceleration of    1 m/s2   directed vertically upwards.

Solution

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(4) In the electric motor of an UFO that fell down in Cuzco, Peru, an electric condenser was found. The condenser consisted of two parallel plates of 20 cm x 30 cm, and between them an electric field of 50000 N/C was detected. Determine the electric charge in each plate.

Solution

(5) Between two vertical parallel plates loaded with opposite electric charges of the same magnitude, an electric field of magnitude Eo has been established.   A little ball of mass m and positive charge Qo   is placed at rest at a position (xo ,yo) between the plates and, it is displaced due to the electric field and to the gravity. Determine the components (x,y) of the position and (Vx,Vy) of the velocity of the little ball a time t after it has been placed. Show that the trajectory of the little ball inside the plates is a straight line.

Solution

The charged particle is horizontally accelerated by the horizontal electric field between the plates and vertically accelerated by the acceleration of the gravity, which is downwards. Since the particle is simply placed, its initial velocity is zero (Vox = Voy = 0):